Relativity Amd The Faraday Disk

Though space limitations prohibit a full theoretical analysis, most treatments of the HPG and the OPFG reviewed start with the Lorentz force to calculate the E field (E = v X B) and measurable voltage (emf). However, Becker notes in regards to the HPG, "we need the concept of the Lorentz force which is foreign to the Maxwell theory but is derivable by relativity theory" [23]. Then the nonvanishing divergence of the HPG effective electric field (E=Bwr, where w is the angular velocity) leads to a volume charge density for the generator, which correlates with the electrostatic field derived earlier. Library research revealed that special relativity can be used to describe the HPG and the OPFG, through use of the polarization/magnetization vectors of electromag-netism which are oppositely paired [24]. However, since the rotating disk is truly a non-inertial reference frame, general relativity must strict-

Figure 1

RELATIVITY COMPARISONS i

Rectilinear Motion

Circular Motion

• No voltage developed when bar and meter move together

• Voltage not developed when disk and meter move together. but etccrnc field is generated 1

- No difference between mouon of observe; and charge: M. = v * ,»

• Difference between rouune charged sphere or rotating observer (Schiff, 1939) B Field vs. no field • Ring currents developed causing magneuc field for sphere rouuon l

• No absolute mouon delectable

• Absolute Rouuon measured (wn tneruaJ ! frame) Saenac. Mannov; see Mannov. Foun-dations of Phvsic< Vol. 8. 1978 p.137

'• SpeciaJ Relauvuy applies

• SpeciaJ relauvitv doesn't apply

• No voiume chargc by spcctaJ relatmty trans-formauon Laws

• Volume charge: E « v » b pB VD p ■ - 2r,wB

• No forces for uniform, constant velocity

• Centn/ucaJ and conobs forces feneraied

ly be used [25]. Fortunately, since the curvature tensor vanishes, space is flat and the Lorentz metric is applicable, though various authors derive slightly different results using general relativity [26], A table has been assembled to summarize the interesting relativistic facts that various authors have contributed to this subject (Fig. 2) [2.7).

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